Collisions that induce melting and vaporization can have a substantial effect on the thermal and geochemical evolution of planets. However, the thermodynamics of major minerals are not well known at the extreme conditions attained during planet formation. We obtained new data at the Sandia Z Machine and use published thermodynamic data for the major mineral forsterite (Mg2SiO4) to calculate the specific entropy in the liquid region of the principal Hugoniot. We use our calculated specific entropy of shocked forsterite, and revised entropies for shocked silica, to determine the critical impact velocities for melting or vaporization upon decompression from the shocked state to 1 bar and the triple points, which are near the pressures of the solar nebula. We also demonstrate the importance of the initial temperature on the criteria for vaporization. Applying these results to N-body simulations of terrestrial planet formation, we find that up to 20% to 40% of the total system mass is processed through collisions with velocities that exceed the criteria for incipient vaporization at the triple point. Vaporizing collisions between small bodies are an important component of terrestrial planet formation.
The properties of silica (SiO 2) at extreme conditions have important applications for planetary processes and for high pressure research. We report the results of 125 plate impact shock compression experiments on fused silica spanning 200-1100 GPa using the Z machine at Sandia National Laboratories. Additionally, we present a complementary set of density functional theory based molecular dynamics calculations based on an amorphous reference state that extend the Hugoniot to 2500 GPa. We find good agreement between the Z data, extant laser driven shock compression experiment data, and computational results over most of the pressure range. With these results, fused silica can be used as a new impedance matching standard for shock compression experiments.
The strength of brittle porous media is of concern in numerous applications, for example, earth penetration, crater formation, and blast loading; thus it is of importance to possess techniques that allow for constitutive model calibration within the laboratory setting. It is the goal of the immediate work to demonstrate an experimental technique allowing for strength assessment, which can be implemented into pressure dependent yield surfaces within numerical simulation schemes. As a case study, the deviatoric strength of distended α-SiO2 has been captured in a tamped Richtmyer- Meshkov instability environment at a pressure regime of 4-10 GPa. In contrast to traditional RMI studies used to infer strength in solids, the described approach herein is implemented to probe the behavior of the porous tamp media backing the corrugated solid surface. Hydrocode simulation has been used to interpret the experiment, and a resulting pressure-dependent yield surface akin to the often employed Modified Drucker-Prager model has been calibrated via the coupled experiment and simulation. The simulations indicate that the resulting jet length generated by the RMI is highly sensitive to the porous media strength, thereby providing a feasible experimental platform capable of capturing pressurized granular deviatoric response. Additionally, a Mach lens loading environment has also been implemented as a validation case study, demonstrating good agreement between experiment and simulation within an alternative loading environment. Calibration and validation of the pressure-dependent yield surface gives confidence to the model form, thereby providing a framework for future porous media strength studies.
Forsterite (Mg2SiO4) single crystals were shock compressed to pressures between 200 and 950 GPa using independent plate-impact steady shocks and laser-driven decaying shock compression experiments. Additionally, we performed density functional theory-based molecular dynamics to aid interpretation of the experimental data and to investigate possible phase transformations and phase separations along the Hugoniot. We show that the experimentally obtained Hugoniot cannot distinguish between a pure liquid Mg2SiO4 and an assemblage of solid MgO plus liquid magnesium silicate. The measured reflectivity is nonzero and increases with pressure, which implies that the liquid is a poor electrical conductor at low pressures and that the conductivity increases with pressure.
The shock Hugoniot for full-density and porous CeO2 was investigated in the liquid regime using ab initio molecular dynamics (AIMD) simulations with Erpenbeck's approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled by carrying out NVT simulations for isotherms between 6000 and 100 000 K and densities ranging from ρ=2.5 to 20g/cm3. The impact of on-site Coulomb interaction corrections +U on the equation of state (EOS) obtained from AIMD simulations was assessed by direct comparison with results from standard density functional theory simulations. Classical molecular dynamics (CMD) simulations were also performed to model atomic-scale shock compression of larger porous CeO2 models. Results from AIMD and CMD compression simulations compare favorably with Z-machine shock data to 525 GPa and gas-gun data to 109 GPa for porous CeO2 samples. Using results from AIMD simulations, an accurate liquid-regime Mie-Grüneisen EOS was built for CeO2. In addition, a revised multiphase SESAME-Type EOS was constrained using AIMD results and experimental data generated in this work. This study demonstrates the necessity of acquiring data in the porous regime to increase the reliability of existing analytical EOS models.